Helen Zia, the American-born child of Chinese immigrants, is talking with two high school friends, one a black girl named Rose, the other a white girl named Julie. It is the 1960's. The subject is civil rights. Zia doesn't recount the details of the conversation, but she remembers that suddenly, to her great astonishment, Rose announces, ''Helen, you've got to decide if you're black or white.''

Today, that choice sounds anachronistic. But it also remains a metaphor for the predicament of people like Zia. The race name lately assigned to them -- Asian-American -- is a shifting, unstable thing, as race names tend to be. Sometimes Asian-Americans figure prominently, as in debates over affirmative action. Sometimes they are simply invisible, as in opinion polls that catalog Americans as black, white, Hispanic and other.

That anxious adolescent conversation also contains the premise of ''Asian American Dreams: The Emergence of an American People.'' Zia's goal seems to be threefold: to argue that Asian-Americans, collectively the fastest growing group in the country, count as an American category; to illuminate some of the fissures among them; and to highlight recent episodes that have shaped the idea of the Asian in America.

The book is part memoir, part social history. Because it is polemical in tone, the rich ordinariness of the many Asian-American lives Zia describes, not least her own, sometimes gets lost. And much of the information here will be familiar to scholars of Asian-American history. Still, this is an important book because it seeks to answer a question that few other popular works pose: What does it take for people like the author to become fully American?

A journalist and a contributing editor to Ms. magazine, Zia grew up in the 1950's and 60's in New Jersey. At the time, Asian faces were so rare that people ''would stop what they were doing to gawk rudely at my family wherever we went.'' Like many immigrant parents, hers pressed their children to speak only English while at the same time teaching them pride in their Chineseness. But ''what Mom and Dad couldn't tell us,'' Zia writes, ''was what it meant to be Chinese in America.''

Zia begins each chapter with a personal narrative, then examines an incident designed to illuminate some aspect of Asian-American life. Some of the personal history is remarkably revealing. When she was 12, she recalls, a Swedish pen pal requested a picture and Zia, afraid that a picture would reveal that she was Chinese, not a typical American, stopped the correspondence altogether. During the Vietnam War, she tells us, a high school classmate couldn't look at her because she reminded the classmate of the war that had killed her brother.

The main body of the book begins with a history of Asians in America, chronicling the lynching of Chinese in late-19th-century California and the restriction of immigration by the Chinese Exclusion Act of 1882. Some of the details are astonishing, but they would have benefited from citations. Zia asserts, for instance, that Japanese-American soldiers were among the first to liberate Dachau but never got credit, and that at home more than 4,000 Japanese-Americans were punished when they refused to take ''loyalty tests,'' forswearing their allegiance to the emperor of Japan.

Most revealing in this section is the way in which Asians, through such episodes, came to find their places on America's racial ladder. A lawsuit brought by a Chinese-American man, Wong Kim Ark, codified the principle of citizenship as a birthright in 1898. Twenty years later, an Indian immigrant in Oregon, Bhagat Singh Thind, challenged a law barring Asians from becoming naturalized citizens, arguing that Indians were of Aryan stock, and thus not Asians; the Supreme Court ultimately ruled against him, concluding that Indians were not white.

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The strongest chapter of the book, not surprisingly, concerns the 1982 murder of the Chinese-American Vincent Chin in Detroit. It is a story Zia knows well. She was living in Detroit at the time and the incident thrust her into making Asian-American history.

Chin's troubles began during an archetypal American ritual: it was a week before his wedding and he was at a strip club with friends. Two men at the club, both auto workers, apparently mistook Chin for Japanese, and they held Japan responsible for the crisis in the American auto industry. They followed Chin out of the bar and clubbed him to death with a baseball bat. Both pleaded guilty and were sentenced to three years probation and $3,780 in fines.

The sentence incensed Detroit's small Asian-American community. But while some urged federal prosecutors to pursue a civil rights case against the two men, others were reluctant -- afraid, Zia says, to ''cast their lot with the more vulnerable position of minorities seeking civil rights.'' She writes that ''behind the discomfort of 'talking about race' was the question of where Asian-Americans fit in America and, more important, where we wanted to be.''

In subsequent chapters, Zia sets out to show how other flash points have marked the development of Asian-Americanness. Her results are mixed.

There is an insightful chapter on the 1992 riots in Los Angeles, when Korean shopkeepers became a target of looters and younger Korean-Americans found themselves suddenly having to speak on behalf of their immigrant parents. Another valuable chapter is devoted to Filipino cannery workers in Alaska fighting against unequal pay and inferior working conditions and learning hard political lessons. The less successful chapters concern cultural debates among Asian-Americans. The subject is a legitimate one, but the discussion here is less nuanced than elsewhere in the book.

It should be noted that there are probably some Americans with Asian roots who do not embrace the pan-Asian-American label. Perhaps as a way to face the black-white choice from her high school days, Zia emphatically does, claiming it as a home, and seeking to show why Asian- Americans matter. In the end, that insistence may be the most significant lesson of this book -- that in the complicated caste and color system of this country, it means something to have a name and to know what that name means.